OPINION
BOGGS, Circuit Judge.Defendant Midwest Specialties, Inc., along with an affiliate and several of its officers and employees (collectively, “Midwest”), appeals a district court order granting summary judgment in favor of the United States on claims that Midwest violated the False Claims Act by providing brake shoes for United States Army jeeps that did not conform to contractual testing requirements. We affirm.
I
In February 1986, Midwest entered into contract DAAE07-86-C-0755 to sell 31,516 jeep brake-shoe kits to the United States Army. The contract required that the brake shoes be welded together with long strips of weld material known as fillet welds. In late March 1986, Midwest requested permission from the Army to “plug weld” the brake shoes instead of fillet welding them. Midwest prepared and submitted to the Army a document marked “Request for Deviation/Waiver MID-0755-1.” Among other things, the deviation request added to the contract a quality-assurance testing requirement, presumably (though it is immaterial) to ensure that the plug welds would be as durable as the originally specified fillet welds. The quality testing requirement in Midwest’s deviation request reads as follows: “Add: Test per Method I or II (attached).” Midwest then attached pages from a deviation request submitted in connection with a different contract several years earlier, as well as schematic diagrams depicting the two required testing methods. The attached pages *298described both the testing specifications and the frequency of the required testing:
1. Slot Welded assembly to be tested to verify that it shall withstand, without failure or cracking, a shear force of 5,000 pounds applied at both ends of the assembly in the tangential direction of the table at points of application. Test sample size shall be three out of the first ten; and thereafter, one out of every 250.
2. Each Slot Welded assembly to be checked to verify that the surfaces of table and web shall conform within 0.005 inches from the ideal. The frequency of inspection will be changed when a level of confidence is established that Midwest Specialties, Inc., has met the required design condition on a repeated basis. The Quality Assurance Representative [a Defense Department contracting employee] can then establish a random sampling check.
Joint Appendix (“J.A.”) at 353.
The Army approved Midwest’s deviation request and issued a contract modification incorporating the terms of deviation request MID0755-1. The Army’s approval document states that the “purpose of this modification is to incorporate deviation #0755-1 (DD Form 1694 attached),” referring to Midwest’s form request for deviation. However, this document did not actually attach Midwest’s deviation request. In January 1987, Midwest entered into another contract (#DAAE07-87-C-0839) to sell 2,552 additional jeep brake shoes to the Army. The Army then approved Midwest’s request to plug weld and test these brake shoes under the same terms as the first jeep brake-shoe contract.
Midwest does not appear to dispute that it did not test one out of every 250 brake-shoe kits manufactured for the Army as required under the contract. This lack of testing did not stop Midwest from delivering the kits, however; between 1987 and 1988, Midwest delivered to the Army 34,068 plug-welded brake-shoe kits under the two contracts at issue. As each batch of brake-shoe kits was delivered, Midwest presented a separate invoice to an Army contracting officer (Gary Martin) — 13 in all — each of which included a statement that the brake shoes conformed to the contracts. Mr. Martin approved these invoices, and as a result the government paid Midwest a total of $1,369,042.40.
In late 1989, the brakes on an Army jeep apparently failed when the welds on one of its Midwest brake shoes faded.1 The Army therefore commenced an investigation of the brake shoes delivered by Midwest. The Army subjected a sample of 18 brake-shoe kits to the Method I test and a sample of 54 kits to the Method II test; the results (as described in an Army memorandum issued on January 22, 1990) indicated that roughly 78 percent of the brake shoes failed to pass muster under the Method I test, and more than 60 percent of the brakes faded the Method II test. The Army investigators concluded that “a rework is needed to upgrade the strength of the [brake] assembly----” See J.A. at 389. As a result, on March 15, 1990, the Army sent out an “inspection emergency” message to ad military bases and embassies around the world ordering that jeeps equipped with brake shoes manufactured by Midwest be “deadlined” un-td replacement brake shoes could be instad-ed. See id. at 322. Since the transmission of that message, ad Midwest brake shoes have been removed from Army jeeps, and those brake shoes are now sitting in warehouses at various United States military installations around the world.
II
One theme of Midwest’s appeal is that the district court’s summary-judgment ruling came as a surprise, with insufficient opportunity for discovery and briefing. We therefore recount in detad the procedural history of this case. In February 1991, Lyle Compton (a former employee of Midwest) filed this action under the qui tam provisions of the False Claims Act, 31 U.S.C. § 3729 et seq., alleging a number of violations of the False Claims Act other than the jeep brake shoe issue described above. In a qui tam action, a private relator files a lawsuit on behalf of *299the United States and may collect a portion of the government’s recovery. See, e.g., United States ex rel. Taxpayers Against Fraud v. General Electric Co., 41 F.3d 1032, 1035 (6th Cir.1994). The United States intervened in September 1992, and in December 1992 filed an amended complaint including allegations relating to the jeep brake shoes.
Over the next two years or so, the government served Midwest with various interrogatories and document requests. The government also took the deposition of Richard Kennedy, Midwest’s president. There is no evidence in the joint appendix that Midwest served the government with any discovery requests at all, though in its brief Midwest asserts that it asked the government to produce certain documents relating to the technical requirements for the brake-shoe kits. Midwest also did not notice any depositions in the case.
After a discovery conference in early April 1995, the district court ordered the parties to brief three legal questions: (1) whether Midwest’s presentation to the government of claims for payment under the jeep brake-shoe contracts would render Midwest liable under the False Claims Act if Midwest knowingly and materially failed to perform the tests required under the contracts; (2) whether, if so, the government would be entitled to recover the full contract price; and (3) what obligations Midwest assumed to test the brake-shoe kits by virtue of the contracts. The parties agree that the court stayed discovery pending the briefing of these questions, although the court’s order does not include any provision staying discovery.
On May 26,1995, Midwest and the government each filed a brief pursuant to the district court’s briefing order. Midwest submitted a four-page brief devoted solely to the question of the proper measure of damages— in effect, addressing only the second question identified in the district court’s order. The government submitted a 22-page “motion for partial summary judgment and memorandum of law,” to which were attached 13 exhibits. The government argued in its partial summary judgment brief that the contracts in question required Midwest to test one of every 250 brake shoes, that it was undisputed that Midwest did not actually perform the required production testing, and that Midwest’s act of submitting invoices for the untested brake shoes constituted a violation of the False Claims Act. In sum, the government’s brief addressed the first and third questions identified in the district court’s briefing order.
On June 21, 1995, the government took a position on the district court’s second question by filing a brief in opposition to Midwest’s brief on the measure of damages. Midwest then filed a brief on July 6, 1995, arguing alternatively that the contracts imposed no testing requirement or that Midwest complied with any applicable requirements. Midwest attached nine exhibits, including government documents, to this brief. On July 31, 1995, the government filed a reply brief on the liability issues discussed in its partial summary judgment brief, and on August 1, 1995, Midwest filed a reply brief on the damages issues discussed in its opening brief. The government then filed a surreply brief on the damages question on August 10, 1995.
On September 26, 1995, the district court granted summary judgment in favor of the government “on the issue of whether defendant was required to perform weld shear tests on one out of every 250 brake shoes sold under the jeep contracts____” The next day, the district court issued an order finding that, in the event Midwest was found liable for violating the False Claims Act, Midwest’s liability would be three times the contract price (a total of $4,107,127.20).
Pursuant to a previous court order, Midwest filed a supplemental brief on October 27, 1995, in which it argued that a genuine issue of fact existed as to “what testing was done” on the brake shoes at issue or, alternatively, that the district court should grant additional time for discovery on the testing issue. The government responded to Midwest’s supplemental brief by filing a reply brief on November 9, 1995, in which it argued for the first time that Midwest actually failed to test in accordance with contract *300requirements and therefore that the record was sufficient for the district court to enter judgment for the United States on its claims under the False Claims Act. The district court responded on November 22, 1995, by permitting Midwest additional time for discovery, and ordering any additional Midwest brief to be filed by January 15,1996.
Midwest failed to comply with the January 15 deadline. On January 18, 1996, Midwest asked the district court for additional time on the ground that “Defendants’ counsel was unaware, until late in the day on Sunday, January 14, 1996, that the Court had issued its September 27, 1995 Memorandum or that the Government had filed its November 7, 1995 Reply Brief.” The government responded in a brief filed on January 25, 1996, that there was no basis for any further delay and that the record as it stood was sufficient to warrant summary judgment in favor of the United States. On January 29, 1996, Midwest filed a 30-page brief asking the district court to reconsider its orders of September 26 and 27, 1995. The apparent purpose of this brief was to relitigate the questions of damages and contract requirements that previously had been resolved by the district court. In an order dated February 13, 1996, the district court essentially rejected Midwest’s motion for reconsideration. It also entered summary judgment in favor of the government on its contention that Midwest failed to conduct testing as required by the contracts, and granted Midwest a limited additional period in which to take discovery relating to whether Midwest’s submission of false claims was “knowing” within the meaning of the False Claims Act.
The parties briefed the “knowing” issue in May and June 1996. Then, on June 20,1996, Midwest asked the district court to request an advisory opinion from the Armed Services Board of Contract Appeals as to whether production testing was required under the contract, what kind of testing was required, and whether Midwest’s brake shoes met the requirements of the contract — in other words, to permit the parties to relitigate before the Board of Contract Appeals each issue already resolved by the district court. The government opposed this motion, and the district court denied it as untimely, stating that “[h]ad the defendant made that request at the outset of the case, it may have had some merit; coming as it has long after I decided critical issues against the defendant, there is no reason, in my view, to seek such opinion.” The district court then held that Midwest had knowingly submitted false claims to the government, and granted the government’s summary judgment motion in its entirety. The parties then filed briefs relating to the government’s proposed form of judgment. The district court entered a final, appealable judgment pursuant to Fed. R.Civ.P. 54(b),2 and this appeal followed.
Ill
Aside from Midwest’s assertion that its right to take discovery was improperly limited by the district court, an allegation we hold is fully refuted by the procedural history outlined above,3 this appeal requires us to resolve two questions: first, whether the record supports the district court’s finding at the summary judgment stage that Midwest knowingly submitted a false claim to the government in violation of the False Claims Act; and second, whether the district court correctly computed Midwest’s liability as treble the full contract price. We consider each question in turn.
A
1
The False Claims Act imposes liability on persons and entities who “knowingly pres*301ent[], or cause[] to be presented, to an officer or employee of the United States Government or a member of the Armed Forces of the United States a false or fraudulent claim for payment or approval.” 31 U.S.C. § 3729. Here, it is undisputed that Midwest presented to a government employee invoices for jeep brake shoes delivered under the jeep brake-shoe contracts. The liability issues presented by Midwest’s appeal are, first, whether the invoices were “false” — ie., whether they incorrectly represented that the brake-shoe kits conformed to the contracts; and second, if so, whether Midwest’s false representation was “knowing.”
Although Midwest strives to portray the contracts as unclear with respect to Midwest’s obligation to “production-test” the jeep brake shoes, the contracts in fact are unambiguous. The parties agree that the original contract (a copy of which is not included in the Joint Appendix) obligated Midwest to deliver fillet-welded brake shoes, but did not require any particular production testing. Midwest then requested a deviation from the original contract terms. Midwest’s deviation request called for the fillet-weld requirement to be replaced by a plug-weld requirement, with the proviso that the brake shoes would be tested under one of two explicitly described test methodologies. See J.A. at 352. The test methods were described in an attachment to Midwest’s deviation request, and the record clearly demonstrates that they were incorporated into the contract. The deviation request stated “Add: Test per Method I or II (attached).” Ibid. The deviation request also contained a narrative justification for the request, which stated that the request was expected to “[ijmprove quality with no reduction in strength,” and which stated a precedent for using plug-welding along with the specified test methods: “This optional welding and test method was approved for Brake Shoe Assembly, 8757663, which is a much heavier shoe for the 5 Ton Truck (see attached Deviation H279-' D2 and approval and test methods).” Ibid. (emphasis added).
The referenced deviation, H279-D2, was attached to Midwest’s deviation request. See id. at 353. It specifically states that three out of the first ten and then one out of each successive 250 brake shoes would be tested. See ibid. This testing frequency could be modified, but only with the approval of the government’s Quality Assurance Representative once a certain level of quality was established. See ibid. Accordingly, on several occasions the district court ruled that the contracts unambiguously imposed a periodic production-testing requirement on Midwest. See, e.g., id. at 484 (holding on September 26, 1995, that “[tjhe tests to be performed are clearly and specifically delineated in the jeep brake shoe contracts as modified”), 799 (holding on September 3,1996, that “[ajfter drafting the testing requirements, which I have found to be unambiguous ... the defendant did not fulfill its obligation to test in accordance with the contract.”). We agree with the district court that the contracts as modified by Midwest’s deviation request contained an express production-testing requirement.
Midwest argues on appeal that, despite the express language contained in its deviation request, it was never obligated to test its brake shoes at all. We are not persuaded by Midwest’s arguments. For example, Midwest argues that the district court itself found the contracts at issue to be ambiguous, and that summary judgment therefore was inappropriate as a matter of law. See Brief of Appellant at 25. In the district court ruling cited by Midwest, however, the court actually found the contract to be unambiguous, noting that Midwest was attempting to create an ambiguity in the contract by arguing that, because the government’s approval of Midwest’s deviation request did not actually attach the test methodologies that had been attached to the deviation request itself, the word “attached” in the approval document had no meaning. See J.A. at 481. Further, Midwest argues that the district court erred in failing to credit the “expert” testimony Midwest proffered for the proposition that the contract, properly interpreted, did not require production testing of the brake-shoe kits. See Brief of Appellant at 28. But, of course, “ ‘experts’ may not testify as to the legal effect of a contract.” CMI-Trading, Inc. v. *302Quantum Air, Inc., 98 F.3d 887, 890 (6th Cir.1996); see also Crow Tribe of Indians v. Racicot, 87 F.3d 1039, 1045 (9th Cir.1996) (“The interpretation of a contract is an issue of law which this court reviews de novo.... Expert testimony is not proper for issues of law.”).
Midwest also argues that it would be improper to hold it liable under a jeep brake-shoe contract for its failure to comply with a testing method originally adopted in a contract for much-heavier five-ton-truck brake shoes, when the jeep brake shoes delivered by Midwest satisfied the 5,000-pound shearing resistance requirement even though they were not properly tested. This argument fails for several reasons. First, parties that contract with the government are held to the letter of the contract — irrespective of whether the contract terms appear onerous from an ex post perspective, or whether the contract’s purpose could be effectuated in some other way — under the maxim that “[m]en must turn square corners when they deal with the Government.” See, e.g., Federal Crop Ins. Corp. v. Merrill, 332 U.S. 380, 384, 68 S.Ct. 1, 3, 92 L.Ed. 10 (1947) (denying crop insurance benefits to farmer who failed to comply with technical requirement of federal crop insurance program, despite substantial compliance with substantive provisions of program); Rock Island, A. & L.R. Co. v. United States, 254 U.S. 141, 143, 41 S.Ct. 55, 56, 65 L.Ed. 188 (1920) (holding failure to comply with “purely formal conditions” fatal to petitioner’s claim for tax refund).4 Second, Midwest, the drafter of the deviation request that included the production-testing requirement, cannot be heard to dispute the legitimacy of the testing requirement. See, e.g., Bush v. Metropolitan Life Ins. Co., 656 F.2d 231, 233 (6th Cir.1981). Third, as a factual matter, Midwest’s brake shoes decidedly did not comply with the 5,000-pound shearing resistance requirement; the summary judgment record indicates that more than 60 percent of the brake shoes tested in an Army investigation failed this requirement. See J.A. at 388.5 Midwest’s only evidence to the contrary is the unsubstantiated assertion of its president, which by itself is insufficient to defeat the government’s summary judgment motion.
Finally, Midwest directs our attention to extrinsic evidence {e.g., the affidavit of Richard Kennedy, Midwest’s president) introduced in the district court to show that the parties did not intend to incorporate a production-testing requirement into the jeep brake shoe contracts. Mr. Kennedy stated in his affidavit that “I do not believe that [the jeep brake shoe contracts] required any production weld shear testing.” See J.A. at 651. However, Kennedy previously testified under oath that “the terms of the contract, of deviation 0755-1, were included into the contract as terms, and all the requirements of deviation H279-D2 and D3 are incorporated into the terms of the contract, which includes the quality assurance tests of shear. ...” Id. at 694 (emphasis added). Kennedy’s deposition testimony is consistent with the stipulated position stated by Midwest’s attorney, that “at the time we believed that we were obligated to test under the little shoe [contract] [i.e., the jeep brake-shoe contract] like we were required to test previously under the big shoe [contract] [i.e., the five-ton truck brake-shoe contract], but clearly to the same requirements.” Id. at 708. As the govern*303ment correctly points out, a party cannot avoid summary judgment through the introduction of self-serving affidavits that contradict prior sworn testimony. See, e.g., Dotson v. U.S. Postal Service, 977 F.2d 976, 978 (6th Cir.), cert. denied, 506 U.S. 892, 113 S.Ct. 263, 121 L.Ed.2d 193 (1992); Gagne v. Northwestern Nat’l Ins. Co., 881 F.2d 309, 315 (6th Cir.1989). In sum, we have 'no difficulty concluding that the summary judgment record was sufficient to support the district court’s holding that Midwest was contractually obligated to test one of every 250 brake shoes produced under the contracts.
2
The district court held that Midwest did not perform the testing required under the jeep brake shoe contracts. Midwest appeared to concede the issue in its appellate brief, arguing variously that it did not know it was required to conduct tests, see Brief of Appellant at 11, that it never told the government it conducted any testing, see id. at 18, and that the parties’ actions were inconsistent with a testing requirement.6 In the district court proceedings, Midwest produced only the affidavit of a single employee who claimed to have conducted some testing (though not the testing specified in the contracts) on some jeep brake shoes (though not at the one-of-every-250 rate required under the contract). The district court ruled that this single affidavit was insufficient to create a genuine issue of material fact, and that the inability of Midwest to produce any other evidence of testing (despite a discovery extension to develop such evidence) was fatal to Midwest’s position:
Absolutely no admissible evidence has been produced by the defendants to show that they performed tests in accordance with the contract. To the extent that the ex parte Nedderman [affidavit] shows that some testing was performed, it is clear that those tests (which were substantially fewer in number than called for by the contract) did not involve the series of three applications called for- in the contract. Aside from the Nedderman [affidavit], which does not show tests in conformance with the contract, the defendants have not produced any evidence to show that tests of that sort were performed at any time.
J.A. at 615-16. Against this backdrop, we agree with the district court that there was no genuine dispute as to Midwest’s failure to perform the required production testing.
3
Having concluded that the summary judgment record supports the district court’s finding that Midwest failed to comply with a testing requirement imposed by the contracts, it remains only for us to determine whether Midwest knowingly submitted false claims to the government for payment under the contracts. As amended in 1986, the False Claims Act provides that “knowing and knowingly ... mean that a person, with respect to information ... (1) has actual knowledge of the information^] (2) acts in deliberate ignorance of the truth or falsity of the information^] or (3) acts in reckless disregard of the truth or falsity of the information, and no proof of specific intent to defraud is required.” 31 U.S.C. § 3729(b).7
The archetypal qui tam [False Claims Act] action is filed by an insider at a private company who discovers his employer has overcharged under a government contract. See, e.g., United States ex rel. Green v. Northrop Corp., 59 F.3d 953 (9th Cir.1995), cert. denied, 518 U.S. 1018, 116 S.Ct. 2550, 135 L.Ed.2d 1069 (1996). However, [False Claims Act] actions have also been sus*304tained under theories of supplying substandard produets or services (see, e.g., United States v. Aerodex, 469 F.2d 1003 (5th Cir.1972)); false negotiation, including bid rigging and defective pricing (see, e.g., United States v. Ehrlich, 643 F.2d 634 (9th Cir.), cert. denied, 454 U.S. 940, 102 S.Ct. 474, 70 L.Ed.2d 247 (1981)); and false certification (see, e.g., United States v. Hibbs, 568 F.2d 347 (3d Cir.1977)).
United States ex rel. Hopper v. Anton, 91 F.3d 1261, 1266 (9th Cir.1996).
Midwest correctly argues that a mere breach of contract, without any evidence of scienter, is insufficient to establish liability under the False Claims Act. However, even pre-1986 precedent makes clear that a manufacturer who knowingly supplies nonconforming goods to the government, based on a belief that the nonconforming goods are just as good as the goods specified in the contract, is liable. See, e.g., Aerodex, 469 F.2d at 1007 (affirming False Claims Act liability of manufacturer who knowingly supplied nonconforming ball bearings, although ball bearings supplied had same basic performance characteristics); United States v. National Wholesalers, 236 F.2d 944 (9th Cir.1956), cert. denied, 353 U.S. 930, 77 S.Ct. 719, 1 L.Ed.2d 724 (1957) (to same general effect). Here, the record convinces us that Midwest had at least a reckless disregard for the falsity of its claims for payment for the jeep brake-shoe kits. Midwest drafted the deviation request specifying periodic production testing of the plug welds. Midwest’s president testified in his deposition that he knew the plug-welded brake shoes were subject to the testing requirement. Despite knowledge of this requirement, Midwest did not test the brake shoes as required by the contracts. Midwest then submitted claims for payment to the government attesting that the brake-shoe kits conformed to contract requirements. This is sufficient to constitute “reckless disregard” of the truth of its representations as to contract compliance. The district court therefore did not err in finding that Midwest violated the False Claims Act.
B
The False Claims Act provides that violators are subject to a civil penalty of between $5,000 and $10,000, plus three times the government’s actual damages. See 31 U.S.C. § 3729(a). Damages awarded under the False Claims Act typically are liberally calculated to ensure that they “afford the government complete indemnity for the injuries done it.” United States ex rel. Marcus v. Hess, 317 U.S. 537, 549, 63 S.Ct. 379, 387, 87 L.Ed. 443 (1943). Midwest does not dispute its liability for a civil penalty, nor does it contest the award of treble damages under the act. Midwest’s sole dispute on appeal as to damages is that the district court should have calculated damages as the difference between the market value of the brake shoe kits as delivered and the value of the kits as promised, rather than awarding the government damages equalling the full contract price.
Whether calculated by the formula urged by Midwest, or as a lump sum equalling the contract price of roughly $1,369,042, the district court’s damages calculation was not erroneous. The record demonstrates that the brake shoe kits delivered by Midwest to the Army were completely valueless, not only because most of them could not withstand 5,000 pounds of force, but also because none of them came with the quality assurance of a product that had been subjected to periodic production testing. As soon as the Army’s investigation revealed that more than 60 percent of the brake shoes could not satisfy the contractual specifications, all Midwest-manufactured jeep brake shoes were taken out of service and placed in storage. See J.A. at 321, 491. While Midwest cites several cases supporting the practice of deducting value received by the government from any damages award, even these cases recognize that the government is entitled to full damages where it proves it received no value at all. For example, in United States v. Advance Tool Co., 902 F.Supp. 1011, 1017 (W.D.Mo. 1995), the court declined to award actual damages to the government because it “failed to set forth specific evidence as to whether any of the 1,301 tools were ever used, are still in use, or if any of the tools had any utility whatsoever.” Ibid. Here, by contrast, the undisputed summary judgment record *305shows that, since immediately after discovering the lack of testing, the government has not used any Midwest brake shoes. Permitting the government to recover the contract price thus is consistent both with Midwest’s suggested theory (since the value of the goods promised (about $1.3 million) less the value received by the government (zero) equals the contract price, and with the general rule recognized in the Uniform Commercial Code that a buyer may reject goods outright “if the goods or the tender of delivery fail in any respect to conform to the contract.”) U.C.C. § 2-601.8
IV
For the foregoing reasons, the judgment of the district court is AFFIRMED.
. Midwest questions whether this event actually occurred. Whether it did is immaterial; as explained below, the pertinent fact is that the Army subsequently discovered that a substantial percentage of Midwest's brake-shoe kits were defective.
. As explained above, the claims raised in the relator's complaint included allegations unrelated to the jeep brake shoes. Because the district court's summary judgment order did not dispose of these unrelated claims, the appealability of the order is based on the district court's certification under Rule 54(b).
. We will not reverse an order granting summary judgment on discovery grounds unless it plainly appears that the district court abused its discretion by denying a party the opportunity to obtain documents or other information that would materially affect the viability of that party’s case. See Sierra Club v. Slater, 120 F.3d 623, 637 (6th Cir.1997). We see nothing in the record to support such a conclusion.
. We agree with the Fifth Circuit that the "square-corners” rule applies fully in the False Claims Act context; "[t]he mere fact that the item supplied under contract is as good as the one contracted for does not relieve defendants of liability" if the item does not in fact conform to the express contract terms. United States v. Aerodex, Inc., 469 F.2d 1003, 1007 (5th Cir.1972).
. Midwest’s only response to the government’s data showing that 60 percent of the brake shoes failed the Method I test and that more than 77 percent of the brake shoes failed the Method II test is to say that the government's test results were not properly supported by an affidavit or otherwise properly authenticated. The government first proffered its testing data in its June 21, 1995, brief. Midwest subsequently filed six briefs in the district court proceedings, none of which ever challenged the authenticity of the government’s testing evidence. Midwest's authenticity challenge was raised for the first time on appeal. Under these circumstances, we must conclude that Midwest has waived any objection it may have had to the admissibility of this evidence at the summary judgment stage. See Johnson v. United States Postal Service, 64 F.3d 233, 237 (6th Cir.1995); Wiley v. United States, 20 F.3d 222, 226 (6th Cir.1994).
. The government, by contrast, presented evidence showing that Midwest had a policy of preparing testing records for all production tests performed under government contracts, see J.A. at 164-77, but was unable to produced any records indicating that any weld testing was performed under the contracts. Because [t]he absence of a record of an event that would ordinarily be documented in official records is probative of the fact that the event did not-occur,” Wiley v. United States, 20 F.3d 222, 227 (6th Cir.1994), the record was sufficient to support the district court’s summary judgment decision.
. Prior to the 1986 amendments, we took the position that only actual knowledge of the falsity of a claim was sufficient to constitute a False Claims Act violation. See United States v. Ekelman & Assoc., Inc., 532 F.2d 545, 548 (6th Cir.1976).
. Two additional considerations support this conclusion. First, the district court ordered the government to return the brake shoes to Midwest to the maximum extent possible. See J.A. at 493 ("The government, however, should allow defendants to retake possession of the warehoused brake shoes if defendants wish to, in case they indeed have some value.”) Midwest’s assertion that a contract-price remedy somehow unjustly enriches the government thus is unpersuasive. Second, we agree with the government that Midwest’s argument in favor of a setoff based on value purportedly received would create a perverse incentive system in which government contractors could endanger the lives of American soldiers by providing substandard materiel, and the Army would be deterred from correcting the danger because it would be forced to bear the cost of any use it received from the substandard goods before their defects were discovered. We stress that the government did not bargain only for plug-welded brake shoes that could withstand a certain amount of force; they also bargained for the confidence that comes with a product that has been subjected to production testing.